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What Is the Fourier Transform?

(www.quantamagazine.org)
474 points rbanffy | 1 comments | | HN request time: 0.198s | source
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anyfoo ◴[] No.45133536[source]
If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform).

This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.

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arethuza ◴[] No.45136059[source]
When I think of Laplace Transforms I always think of control theory - poles, zeros etc.
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kmarc ◴[] No.45136173[source]
Probably that's why we are learning about it in the "Control Theory" classes at university. :-)

Jokes aside, I graduated as "Computer Engineer" (BSc) and then also did a "Master in Computer Science"; I was (young and) angry at the universe why soooo many classical engineering classes and then theory I had to sit through (Control theory, Electrical engineering, Physics), and we never learned about the cool design patterns etc etc.

Today I see that those formative years helped me a lot with how I develop intuition when looking at large (software) systems, and I also understand that those ever changing best design patterns I can (could have) just look up, learn, and practice in my free time.

I wish a today-me would have told my yesterday-me all this.

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arethuza ◴[] No.45136231[source]
I learned about it after I graduated with a CS degree - I mean in true university degree fashion we'd been taught about Laplace and Z transforms (and related things) but with no practical applications.

After graduating I joined an academic research team based mainly in a EE department who were mainly Control Engineers - we were mainly doing stuff around qualitative reasoning and using it for fault diagnosis, training etc.

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1. arethuza ◴[] No.45139258[source]
To be fair (and because I've just remembered - it was ~40 years ago) we did get some practical stuff covered in the maths part of my CS degree in the application of group theory (groups, rings & fields) to coding theory.